US7324706B2 - System and method for representing a general two dimensional spatial transformation - Google Patents
System and method for representing a general two dimensional spatial transformation Download PDFInfo
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- US7324706B2 US7324706B2 US10/939,045 US93904504A US7324706B2 US 7324706 B2 US7324706 B2 US 7324706B2 US 93904504 A US93904504 A US 93904504A US 7324706 B2 US7324706 B2 US 7324706B2
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Abstract
Description
-
- (a) a geometry input interface for obtaining geometric parameters that define the transformation and which include lens parameters describing display optics, projection angles, display panel geometry for flat screen and curved screen, and user specified parameters;
- (b) a grid transformation generator, coupled to said geometry input interface, for generating a grid data transformation that maps the output pixel coordinates onto the input pixel coordinates;
- (c) a patch geometry generator, coupled to said grid transformation generator, for dividing the output pixel coordinate space into a number of corresponding patches according to an underlying geometry, each patch having an associated grid data set, said patch geometry generator determining the boundaries of the output space patches;
- (d) a surface function estimator, coupled to said patch geometry generator, to parameterize the grid data set for each patch as a surface functional represented by surface coefficients; and
- (e) an output interface coupled to the surface function estimator to store the surface coefficients.
-
- (a) obtaining geometric input parameters that define the transformation and that include lens parameters describing display optics, projection angles, display panel geometry for flat screen and curved screen, and user specific parameters;
- (b) generating a grid data transformation based on said geometric input parameters, to map the output pixel coordinates onto the input pixel coordinates;
- (c) dividing the output pixel coordinate space into a number of corresponding patches according to an underlying geometry, each patch having an associated grid dataset and determining the boundaries of the output space patches;
- (d) parameterizing said grid data transformation, in each of the patches, as a surface functional represented by surface coefficients; and storing said surface coefficients.
U=F u(X,Y)
V=F v(X,Y) (1)
and similarly for v, as discussed above. Instead of storing the numerous grid data relation points {(ui,vi),(xi,yi)}, only the surface coefficients Snu,kl need to be stored (i.e. for all surfaces/patches). The surface can then be evaluated to determine the inverse mapped pixel positions. The fitting procedure determines the surface coefficients. Different methods and fitting functions can be used to fit the data, but the most commonly used is the Least Squares method for fitting.
- 1) Geometry of the patch (absolute position of patch origin, patch size)
- 2) Surface coefficients describing surface fit to grid data relation
x→x′=r 1 x, y→y′=s 1 y
u→u′=r 2 u, v→v′=s 2 v (5)
the new surface coefficients for the scaled transformation are:
y A ″=Ky A −K
x A ″=Kx A −K
or
x A=(x A ″+
x A=(y A ″+
{(x1n,y1n),(x2n,y2n)} (14)
{(x1n″,y1n″),(x2n″,y2n″)} (15)
W(n)=Minimum(x2n ″, K
H(n)=Minimum(y2n ″, K
{(
ax 3 +bx 2 +cx+d=((ax+b)x+c)x+d (21)
Claims (44)
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US10/939,045 US7324706B2 (en) | 2004-09-09 | 2004-09-09 | System and method for representing a general two dimensional spatial transformation |
TW094121843A TWI298147B (en) | 2004-09-09 | 2005-06-29 | System and method for representing a general two dimensional spatial transformation |
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US20060050074A1 (en) | 2006-03-09 |
TWI298147B (en) | 2008-06-21 |
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